1-out-of-5 Maximin-Share Allocations Always Exist for Four Agents
For four agents with nonnegative additive valuations, a complete 1-out-of-5 maximin-share allocation always exists, improving the previous 1-out-of-6 guarantee. Together with known exact-MMS counterexamples, this completely characterizes the four-agent case: the guarantee holds exactly for $d\geq5$. The main technical contribution is...